Estimating volume of switching among television programs for an audience measurement panel

ABSTRACT

Disclosed example apparatus to determine volume of switching (VoS) among television programs examine first viewing data associated with a first time period and second viewing data associated with a second time period to identify a first set of panelists represented in both the first and second viewing data; in response to a size of the first set of panelists satisfying both first and second thresholds, estimate the VoS based on a first subset of the first viewing data and a second subset of the second viewing data associated with the first set of panelists; and in response to the size of the first set of panelists satisfying the first but not the second threshold, estimate the VoS based on the first and second subsets, and a third subset of the first viewing data and a fourth subset of the second viewing data associated with a second set of panelists.

RELATED APPLICATION(S)

This patent arises from a continuation of U.S. application Ser. No.17/360,818, titled “ESTIMATING VOLUME OF SWITCHING AMONG TELEVISIONPROGRAMS FOR AN AUDIENCE MEASUREMENT PANEL,” and filed on Jun. 28, 2021,which is a continuation of U.S. application Ser. No. 16/572,135, titled“ESTIMATING VOLUME OF SWITCHING AMONG TELEVISION PROGRAMS FOR ANAUDIENCE MEASUREMENT PANEL,” and filed on Sep. 16, 2019, which is acontinuation of U.S. application Ser. No. 15/799,660, titled “ESTIMATINGVOLUME OF SWITCHING AMONG TELEVISION PROGRAMS FOR AN AUDIENCEMEASUREMENT PANEL,” and filed on Oct. 31, 2017, which claims the benefitof U.S. Provisional Application No. 62/432,332, titled “ESTIMATINGVOLUME OF SWITCHING AMONG TELEVISION PROGRAMS FOR AN AUDIENCEMEASUREMENT PANEL,” and filed on Dec. 9, 2016. Priority to U.S.Provisional Application No. 62/432,332, U.S. application Ser. No.15/799,660, U.S. application Ser. No. 16/572,135 and U.S. applicationSer. No. 17/360,818 is claimed. U.S. Provisional Application No.62/432,332, U.S. application Ser. No. 15/799,660, U.S. application Ser.No. 16/572,135 and U.S. application Ser. No. 17/360,818 are herebyincorporated by reference in their respective entireties.

FIELD OF THE DISCLOSURE

This disclosure relates generally to audience measurement and, moreparticularly, to estimating volume of switching among televisionprograms for an audience measurement panel.

BACKGROUND

A goal of television (TV) program volume of switching (VoS) analysis isto measure and represent the dynamic changes in TV program tuningactivity between two measurement periods using person-level, orpanelist-level, viewing data obtained for an audience measurement panel.In a VoS analysis, each increase (or decrease) in a panelist's programviewing is attributed to corresponding decreases (or increases) inviewing of other program(s) and/or partaking in other activity. VoSanalysis can provide media content providers with insights into viewerbehavior, such as who is watching their programs, what are the competingprograms, how does a given program perform over time, etc.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of an example television program volume ofswitching estimator implemented in accordance with the teachings of thisdisclosure.

FIG. 2 illustrates an example output generated by the example televisionprogram volume of switching estimator of FIG. 1 .

FIGS. 3-5 are flowcharts representative of example computer readableinstructions that may be executed to implement the example televisionprogram volume of switching estimator of FIG. 1 .

FIG. 6 is a block diagram of an example processor platform structured toexecute the example computer readable instructions of FIGS. 3, 4 and/or5 to implement the example television program volume of switchingestimator of FIG. 1 .

The figures are not to scale. Wherever possible, the same referencenumbers will be used throughout the drawing(s) and accompanying writtendescription to refer to the same or like parts, elements, etc.

DETAILED DESCRIPTION

Example methods, apparatus, systems and articles of manufacture (e.g.,non-transitory physical storage media) to estimate volume of switchingamong television programs for an audience measurement panel aredisclosed herein. Example methods disclosed herein to estimate volume ofswitching among television programs include determining, based onaccessed panelist program viewing data, a first volume of switchingvalue representing a portion of a decreased amount of tuning by matchedpanelists to a first program measured from a first measurement period toa second measurement period to attribute to an increased amount oftuning by the matched panelists to a second television program measuredfrom the first measurement period to the second measurement period.Disclosed example methods also include estimating, based on the accessedpanelist program viewing data and the first volume of switching value, asecond volume of switching value representing a portion of a decreasedamount of tuning by unmatched panelists to the first television programmeasured from the first measurement period to the second measurementperiod to attribute to an increased amount of tuning by unmatchedpanelists to the second television program measured from the firstmeasurement period to the second measurement period. Disclosed examplemethods further include combining the first volume of switching valueand the second volume of switching value to determine a third volume ofswitching value corresponding to a combination of the matched panelistsand the unmatched panelists.

In some disclosed examples, the matched panelists correspond to a firstgroup of panelists represented in the program viewing data for both thefirst and second measurement time periods. In some disclosed examples,the unmatched panelists correspond to a second group of panelists notrepresented in the program viewing data for at least one of the first orsecond measurement time periods,

Additionally or alternatively, some disclosed example methods furtherinclude outputting a volume of switching matrix including the thirdvolume of switching value to represent a portion of a decreased amountof tuning by the combination of matched and unmatched panelists to thefirst television program from the first measurement period to the secondmeasurement period to attribute to an increased amount of tuning by thecombination of the matched and unmatched panelists to the secondtelevision program from the first measurement period to the secondmeasurement period.

Additionally or alternatively, in some disclosed example methods, theestimating of the second volume of switching value includes (1)determining, based on the accessed panelist program viewing data, afirst matched tuning value representing an amount of tuning by thematched panelists to the first program in the first measurement period,(2) determining, based on the accessed panelist program viewing data, asecond matched tuning value representing an amount of tuning by thematched panelists to the second program in the first measurement period,(3) determining, based on the accessed panelist program viewing data, afirst unmatched tuning value representing an amount of tuning by theunmatched panelists to the first program in the first measurement period(4) determining, based on the accessed panelist program viewing data, asecond unmatched tuning value representing an amount of tuning by theunmatched panelists to the second program in the first measurementperiod, and (5) determining the second volume of switching value basedon the first volume of switching value, the first matched tuning value,the second matched tuning value, the first unmatched tuning value andthe second unmatched tuning value. In some such disclosed examplemethods, the determining of the second volume of switching value basedon the first volume of switching value, the first matched tuning value,the second matched tuning value, the first unmatched tuning value andthe second unmatched tuning value includes determining a scale factorbased on (i) a first ratio of the first unmatched tuning value to thefirst matched tuning value and (ii) a second ratio of the secondunmatched tuning value to the second matched tuning value, andmultiplying the first volume of switching value by the scale factor todetermine the second volume of switching value. Furthermore, in somesuch disclosed example methods, the determining of the scale factorfurther includes determining a square root of the first ratio multipliedby the second ratio.

Additionally or alternatively, in some such disclosed example methods,the estimating of the second volume of switching value further includessolving for the second volume of switching value based on (i) the resultof the multiplying of the first volume of switching value by the scalefactor, (ii) a first constraint that a first sum of volume of switchingvalues representing tuning by the unmatched panelists from respectiveones of a first set of programs, including the first program, in thefirst measurement period to the second program in the second measurementperiod equals the second unmatched tuning value, and (iii) a secondconstraint that a second sum of volume of switching values representingtuning by the unmatched panelists from the first program in the firstmeasurement period to respective ones of a second set of programs,including the second program, in the second measurement period equalsthe first unmatched tuning value.

These and other example methods, apparatus, systems and articles ofmanufacture (e.g., non-transitory physical storage media) to estimatevolume of switching among television programs for an audiencemeasurement panel are disclosed in greater detail below.

As mentioned above, goal of television (TV) program volume of switching(VoS) analysis is to measure and represent the dynamic changes in TVprogram tuning activity between two measurement periods usingperson-level, or panelist-level, viewing data obtained for an audiencemeasurement panel. In a VoS analysis, each increase (or decrease) in apanelist's program viewing is attributed to corresponding decreases (orincreases) in viewing of other program(s) and/or partaking in otheractivity. VoS analysis can provide media content providers with insightsinto viewer behavior, such as who is watching their programs, what arethe competing programs, how does a given program perform over time, etc.

Prior VoS analysis techniques are limited to using panelist viewing dataonly for matching panelists who are represented in the panelist viewingdata for most, or all, of the two measurement periods of interest. Inother words, prior VoS analysis techniques exclude panelists associatedwith incomplete panelist viewing data from the VoS analysis. In thecontext of VoS analysis, incomplete panelist viewing data generallyoccurs in one of two ways: (1) a matched panelist, who is represented inthe panelist viewing data for the two measurement periods of interest,was included in the panel for just a portion of one or both of themeasurement periods, or (2) an unmatched panelist is represented in thepanelist viewing data for just one of the two measurement periods ofinterest.

Unlike such prior techniques, example VoS analysis techniques disclosedherein are able to utilize incomplete panelist viewing data in the VoSanalysis. For example, for incomplete panelist viewing data associatedwith a matched panelist having missing data from one or both of themeasurement periods, example VoS analysis techniques disclosed hereinperform bias correction to account for the portion of missing data forthe matched panelist. For panelist viewing data associated withunmatched panelists who are missing from one of the measurement periods,example VoS analysis techniques disclosed herein estimate the VoS valuesassociated with such unmatched panelists based on a combination of theVoS values determined for matched panelists and the available panelistviewing data for the unmatched panelists. As such, example VoS analysistechniques disclosed herein improve VoS estimates by including panelistswho are in the audience measurement panel for just a portion of the twomeasurement periods of interest.

Turning to the figures, a block diagram of an example TV program VoSestimator 100 implemented in accordance with the teachings of thisdisclosure is illustrated in FIG. 1 . The example VoS estimator 100includes an example data retriever 105 to obtain example input data 110defining the scope of the VoS analysis to be performed by the VoSestimator 100. The example data retriever 105 also accesses an examplepanelist database 115 to obtain (e.g., retrieve) panelist data (e.g.,such as panelist viewing data including tuning/viewing minutes) for eachof the two measurement periods of the VoS analysis.

The example VoS estimator 100 further includes an example panelistmatcher 120 to match panelists represented in the panelist data for boththe first and second measurement periods to determine matched panelistsand unmatched panelists for the VoS analysis being performed. Inexamples disclosed herein, a matched panelist is a panelist representedin the program viewing data for both the first and second measurementtime periods. In examples disclosed herein, an unmatched panelist is apanelist not represented in the program viewing data for at least one ofthe first or second measurement time periods. In some examples, the VoSestimator 100 considers a panelist to be represented in the programviewing data for a given measurement period when the program viewingdata includes valid data for the panelist over at least a thresholdpercentage of the given measurement period. As disclosed in furtherdetail below, the threshold percentage is referred to as a unificationthreshold.

The example VoS estimator 100 includes an example matched panelist biascorrector 125 to correct for biases resulting from missing panelist datafor the matched panelists identified by the panelist matcher 120, and anexample matched panelist VoS calculator 130 to calculate the VoS valuesrepresenting the program switching performed by the matched panelistsindividually and aggregated. The example VoS estimator 100 furtherincludes an example unmatched panelist VoS estimator 135 to estimate VoSvalues representing the program switching performed by unmatchedpanelists (e.g., in the aggregate), who are panelists identified by thepanelist matcher 120 as missing from either the first measurement periodor the second measurement period. As disclosed in further detail below,the unmatched panelist VoS estimator 135 of the illustrated exampleestimates the VoS values associated with such unmatched panelists basedon a combination of the VoS values determined by the matched panelistVoS calculator 130 for matched panelists, and the available panelistdata for the unmatched panelists.

The example VoS estimator 100 also includes an example VoS outputgenerator 140 to combine the VoS values for the matched panelists andthe unmatched panelists to calculate total VoS values representing theprogram switching performed by the group of matched and unmatchedpanelists (e.g., in the aggregate). The VoS output generator 140 of theillustrated example also provides an example output 145 representing theresults of the VoS analysis. In some examples, the output 145 is in aform capable of being presented via an example output device 150. In theillustrated example, the output device 150 can be implemented by anyoutput device, such as one or more the example output devices 624included in the example processor platform 600 of FIG. 6 , which isdescribed in further detail below.

An example output 145 provided by the VoS estimator 100 for a VoSanalysis is illustrated in FIG. 2 . The example VoS output 200 is aSankey diagram representing the dynamic changes in TV program tuningactivity between two example measurement periods 205 and 210 asdetermined by the VoS estimator 100. As shown in FIG. 2 , in a VoSanalysis, each increase (or decrease) in overall panelist tuning (e.g.,viewing) of a given program is attributed to corresponding decreases (orincreases) in tuning (e.g., viewing) of other program(s) and/orpartaking in other activity.

Returning to the illustrated example of FIG. 1 , the example panelistdatabase 115 of the VoS estimator 100 includes demographic information,such as age, gender, location, income, education, etc., associated withpanelists of statistically selected panelist monitoring sites (e.g.,households) included in an audience measurement panel, such as anational people meter panel managed by The Nielsen Company (US), LLC.The panelist database 115 of the illustrated example also includespanelist measurement data obtained from audience measurement metersmonitoring the statistically selected panelist monitoring sites (e.g.,households). Such panelist measurement data includes, for example,panelist level viewing data identifying the television programspresented (e.g., tuned) at the statistically selected panelistmonitoring sites and their respective durations of presentation. Forexample, the panelist database 115 can include All-Minute RespondentLevel Data (AMRLD) obtained from monitoring the national people meterpanel managed by The Nielsen Company (US), LLC. Additionally oralternatively, in some examples, the panelist database 115 includescensus measurement data typically obtained from a much larger audiencethan the panelist measurement data, such as via set-top box return pathdata corresponding to subscribers of one or more cable serviceproviders, satellite service providers, etc. Such census measurementdata includes, for example, respondent level viewing data identifyingthe television programs presented at each reporting site and theirrespective durations of presentation, but without demographicinformation associated with the respondents. In the illustrated example,the panelist database 115 further includes details concerning theprograms that are potentially available at the statistically selectedpanelist monitoring sites, such as program and episode identificationinformation, program durations, etc.

To determine which panelist data, such as the panelist viewing data, toaccess for a VoS analysis, the data retriever 105 of the illustratedexample accepts several types of example input data 110. In theillustrated example, the input data 110 can be provided via any inputdevice, such as one or more the example input devices 622 included inthe example processor platform 600 of FIG. 6 , which is described infurther detail below. For example, the data retriever 105 accepts inputdata 110 specifying the programs (and/or networks) that are to be thesubject of the VoS analysis. In some examples, it is recommended tovisualize 6 or fewer programs in each measurement period (with thenumber of programs included in each period being the same or different).Also, some or all of the specified programs can be the same or differentacross the two measurement periods. However, in some examples, it isrecommended to select programs having similar durations in the differentperiods because, in some such examples, switching is measured in rawminutes (or some other granularity) rather than average minutes watchedand selecting programs with similar durations may make interpretation ofthe analysis easier.

The input data 110 of the illustrated example also specifies the twomeasurement periods that are to be the subject of the VoS analysis. Insome examples, for each of the two measurement periods, durations of atleast 60 days are recommended. This is because too small of ameasurement period may produce less reliable switching values, lowercarryover values (corresponding to staying on the same program) andhigher switching values to the default “Other” category. The exampleinput data 110 further specifies the gap between the two measurementperiods. In some examples, it is recommended to select measurementperiods with a relatively small gap between them. This is because toolarge of a gap and/or too large of a measurement period may result infewer panelists that are 100% unified, which may result in moreunmatched panelists and/or more matched panelists with missing data,which will need to be adjusted, as disclosed in further detail below,before inclusion in the VoS analysis.

The input data 110 of the illustrated example also specifies a thresholdfor the unification rule to be used for the VoS analysis. Unificationrefers to the percentage of a measurement period that a panelist hasvalid panelist data. For example, a panelist is considered 100% unifiedfor a measurement period if the panelist has valid panelist data overthe entire period. The unification threshold specifies a lowerunification limit to be met to consider a panelist as being included ina given measurement period. In some examples, the default unificationthreshold is 75%.

As mentioned above, the example VoS estimator 100 includes the examplematched panelist bias corrector 125 to correct for biases resulting frommissing panelist data for the matched panelists identified by thepanelist matcher 120. As noted above, a matched panelist is a panelistrepresented in the program viewing data for both the first and secondmeasurement time periods. In some examples, the matched panelist biascorrector 125 removes matched panelists who do not meet the unificationthreshold (e.g., 75%) in both measurement periods. The matched panelistbias corrector 125 of the illustrated example also applies an adjustmentfactor to ensure each matched panelist has equal weights for eachperiod. In some examples, this adjustment factor is applied according toEquations 1 and 2.

$\begin{matrix} & {{Equation}1}\end{matrix}$Adjusted_Person_Program_Minutes_Period_X = Adjustment_Factor * Actual_Person_Program_Minues_Period_X$\begin{matrix} & {{Equation}2}\end{matrix}$${Adjustment\_ Factor} = \frac{\min\left( {{{Person\_ Days}{\_ In}{\_ Tab}{\_ Period}{\_ X}},{{Person\_ Days}{\_ In}{\_ Tab}{\_ Period}{\_ Y}}} \right)}{{Person\_ Days}{\_ In}{\_ Tab}{\_ Period}{\_ X}}$

In Equations 1 and 2, the variable X refers to the measurement periodwith the higher unification percentage for the given matched panelist,and the variable Y refers to the measurement period with the lowerunification percentage for the given matched panelist. Thus, accordingto Equation 2, the adjustment factor (corresponding toAdjustment_Factor) for a matched panelist is determined to be thesmaller of the percentages of time the matched panelist has valid dataover each one of the two measurement periods (corresponding to min(Person_Days_In_Tab_Period_X, Person_Days_In_Tab_Period_Y)) divided bythe larger of the percentages of time the matched panelists has validdata over each one of the two measurement periods (corresponding toPerson_Days_In_Tab_Period_X). Then, the amount of viewing for thematched panelist during the measurement period with the largerpercentage of valid data (corresponding toActual_Person_Program_Minutes_Period_X) is scaled by the determinedadjustment factor according to Equation 1. For example, a matchedpanelist with unification percentages of 100% in period 2 and 90% inperiod 1 will have all period 2 minutes multiplied by 90% to ensureequal weighting in both periods.

In some examples, the percentage of switching between programs remainsfairly consistent as the unification percentages and number of days inthe measurement period (e.g., days-in-tab) increase. However, as thesevalues get smaller, the tuning minutes assigned to or from the default“Other” category may increase, whereas the “Carryover” minutes decrease.“Carryover” refers to switching between the same program (or, in otherwords, remaining with the same program), whereas “Other” refers toswitching between a program and a non-program or some other activity(e.g., a program not specified in the VoS analysis, some other mediaexposure, no media exposure, etc.).

As mentioned above, the example VoS estimator 100 includes the examplematched panelist VoS calculator 130 to calculate the VoS valuesrepresenting the program switching performed by the matched panelistsindividually and aggregated. The matched panelist VoS calculator 130 ofthe illustrated example calculates gains, losses, and volumes ofswitching (e.g., in tuning/viewing minutes) between each pair ofprograms between the two measurement periods. The following is anexample VoS calculation algorithm implemented by the matched panelistVoS calculator 130. The example algorithm is described from theperspective of calculating VoS values for an example matched panelist(referred to as panelist 1).

First, the example matched panelist VoS calculator 130 accesses thepanelist data retrieved by the data retriever 105 to determine theprogram viewing minutes for panelist 1 and for the specified programsand specified measurement periods. For example, assume the programviewing minutes determined for panelist 1 in period 1 are given by Table1.

TABLE 1 ## person_id program_id minutes ## 1: 1 1 20 ## 2: 1 3 10 ## 3:1 4 10Assume the program viewing minutes determined for panelist 1 in period 2are given by Table 2

TABLE 2 ## person_id program_id minutes ## 1: 1 1 10 ## 2: 1 2 10 ## 3:1 4 15In Tables 1 and 2, the column labeled “person_id” includes the personidentifier for the given panelists, the column labeled “program_id”includes the program identifiers for the different programs tuned to bythe panelist identified by the corresponding person identifier, and thecolumn “minutes” includes the amount of time the given panelistidentified by the corresponding person identifier tuned to the givenprogram identified by the corresponding program identifier.

Next, the example matched panelist VoS calculator 130 calculates thecarryover, and increase and/or decrease in program viewing minutes foreach program from the first measurement period (P1) to the secondmeasurement period (P2). For example, for program i, the matchedpanelist VoS calculator 130 calculates Equations 3-5.

Carryover_(i)=min(P1_(i) ,P2_(i))   Equation 3

Increase_(i)=max(P2_(i) −P1_(i),0)   Equation 4

Decrease_(i)=max(P1_(i) −P2_(i),0)   Equation 5

where:

P1_(i): Program i's viewing in measurement period 1;

P2_(i): Program i's viewing in measurement period 2.

An example of calculating the carryover and increase/decrease viewingminutes for panelist 1 using the data of Tables 1 and 2 is given inTable 3:

TABLE 3 ## program_id mins1 mins2 carryover increase decreasetotincrease ## 1: 0 0 5 0 5 0 20 ## 2: 1 20 10 10 0 10 20 ## 3: 2 0 10 010 0 20 ## 4: 3 10 0 0 0 10 20 ## 5: 4 10 15 10 5 0 20In Table 3, the column labeled “program_id” includes the programidentifiers for the different programs tuned to by panelist 1, thecolumn labeled “mins1” includes the amount of time during the firstmeasurement period that panelist 1 tuned to the given program identifiedby the corresponding program identifier, the column labeled “mins2”includes the amount of time during the second measurement period thatpanelist 1 tuned to the given program identified by the correspondingprogram identifier, the column labeled “carryover” includes thecarryover amount of tuning from the first measurement period to thesecond measurement period determined according to Equation 3 for thegiven program identified by the corresponding program identifier, thecolumn labeled “increase” includes the increase in amount of tuning fromthe first measurement period to the second measurement period determinedaccording to Equation 4 for the given program identified by thecorresponding program identifier, the column labeled “decrease” includesthe decrease in amount of tuning from the first measurement period tothe second measurement period determined according to Equation 5 for thegiven program identified by the corresponding program identifier, andthe column labeled “totincrease” includes the sum of the increasedamount of tuning values listed in the column labeled “increase.”

Based on Table 3, the example matched panelist VoS calculator 130determined that panelist 1, for example, spent 20 minutes in period 1and 10 minutes in period 2 watching program 1 (program_id 1). Thus, fromperiod 1 to period 2, panelist 1 spent less time (10 minutes less)watching program 1, with just 10 minutes being a carryover from the sameprogram, program 1, watched in the prior period 1. The other 10 minuteswent to other programs person 1 watched in period 2.

Next, the example matched panelist VoS calculator 130 calculates the VoSvalues for panelist 1, also referred to as the switching volumes forpanelist 1. Switching occurs when a panelist spent more time watchingprogram i in period 1 and less time on watching program j in period 2,or vice versa. The matched panelist VoS calculator 130 of theillustrated example calculates VoS values s_(i,j) for program i inperiod 1 and program j in period 2 according to Equation 6:

$\begin{matrix}{s_{i,j} = {\frac{{Increase}_{j}}{\sum_{k = 1}^{K}{Increase}_{k}}*{Decrease}_{i}}} & {{Equation}6}\end{matrix}$

The VoS value s_(i,j) of Equation 6 represents the portion of thedecrease in the program viewing minutes of program i in period 1(corresponding to the variable Decrease_(i)) to be attributed to theincrease in the program viewing minutes of program j in period 2(corresponding to the variable Increase_(j)).

The matched panelist VoS calculator 130 of the illustrated example alsoutilizes a virtual program (referred to as program 0) as a catch-all torepresent the difference in total viewing minutes between the twomeasurement periods. In the preceding example, panelist 1 spent 40minutes watching three programs in period 1 and 35 minutes watchingthree programs in period 2. Thus, panelist 1's total viewing minutesdecreased by 5 minutes in period 2 relative to period 1, which thematched panelist VoS calculator 130 assigns to program 0, which alsocorresponds to an “Other TV and non-TV” bucket.

An example of calculating the VoS value s_(i,j) for panelist 1 andprogram 1 in period 1 using the data of Table 3 is given in Table 4:

TABLE 4 ## program_id_p1 program_id_p2 decrease increase SumOfIncreaseproportion volume ## 1: 1 0 10 5 20 0.25 2.5 ## 2: 1 1 10 0 20 0.00 10.0## 3: 1 2 10 10 20 0.50 5.0 ## 4: 1 3 10 0 20 0.00 0.0 ## 5: 1 4 10 5 200.25 2.5In Table 4, each row corresponds to a possible switching combination oftuning by panelist 1 from the program labeled by the identifier “programidp1” during the first measurement period to the program labeled by theidentifier “program idp2” during the first measurement period. In Table4, the column labeled “decrease” corresponds to the value of Decreasefrom Equation 6 corresponding to the given possible switchingcombination represented by the given row, the column labeled “increase”corresponds to the value of Increase_(i) from Equation 6 correspondingto the given possible switching combination represented by the givenrow, the column labeled “SumOfIncrease” corresponds to the value ofΣ_(k=1) ^(K) Increase_(k) from Equation 6 corresponding to the givenpossible switching combination represented by the given row, the columnlabeled “proportion” corresponds to the value of Increase_(j)/Σ_(k=1)^(K) Increase_(k) from Equation 6 corresponding to the given possibleswitching combination represented by the given row, and the columnlabeled “volume” corresponds to the resulting VoS value of s_(i,j) fromEquation 6 corresponding to the given possible switching combinationrepresented by the given row.

The example matched panelist VoS calculator 130 then tabulates anexample switching matrix for panelist 1 for the different combinationsof switching from program i in measurement period 1 to program j inmeasurement period 2. An example switching matrix tabulated by thematched panelist VoS calculator 130 of the illustrated example forpanelist 1 using the data of Tables 1-3 and Equation 6 is given in Table5:

TABLE 5 ## program_id_p1 program_id_p2 volume ## 1: 1 0 2.5 ## 2: 1 110.0 ## 3: 1 2 5.0 ## 4: 1 4 2.5 ## 5: 3 0 2.5 ## 6: 3 2 5.0 ## 7: 3 42.5 ## 8: 4 4 10.0

Finally, the example matched panelist VoS calculator 130 aggregates(e.g., sums) the corresponding VoS value s_(i,j) for each matchedpanelist and for each pair of programs to determine aggregate VoS valuesfor the matched panelists. The result is a set of VoS valuesrepresenting a portion of a decreased amount of tuning by matchedpanelists to a first program, i, measured from a first measurementperiod (e.g., period 1) to a second measurement period (e.g., period 2)to attribute to an increased amount of tuning by the matched paneliststo a second television program, j, measured from the first measurementperiod (e.g., period 1) to the second measurement period (e.g., period2).

As mentioned above, the example VoS estimator 100 includes the exampleunmatched panelist VoS estimator 135 to estimate VoS values representingthe program switching performed by unmatched panelists (e.g., in theaggregate), who are panelists identified by the panelist matcher 120 asmissing from either the first measurement period or the secondmeasurement period. Unmatched panelists have viewing data in only one oftwo measurement periods. Therefore, switching cannot be calculated forunmatched panelists in the same manner described above as for matchedpanelists. Nevertheless, unmatched panelists viewing data can be used bythe example unmatched panelist VoS estimator 135 to estimate switchingvolumes for unmatched panelists over the two measurement periods.

An example algorithm implemented by the unmatched panelist VoS estimator135 to estimate VoS values for unmatched panelists is given in Table 6:

TABLE 6 1. For matched panelists, calculate: Total minutes by program bymeasurement period VoS for each pair of programs 2. For unmatchedpanelists, calculate: Total minutes by program by measurement period VoSis not available - this is what is being estimated 3. Estimateproportion-based estimates for VoS for unmatched panelists 4. Optimizethe VoS estimates for unmatched panelists with constraints based upontotal minutes 5. Calculate total VoS by aggregating (e.g., summing)actual VoS for matched panelists and optimized VoS for unmatchedpanelists

In the following disclosure, the following variables are used:

s_(i,j) ^(k): Minutes switched from tuning to program i (in period 1) totuning to program j (in period 2) by a matched panelist k.

s_(i,j): VoS from tuning to program i (in period 1) to tuning to programj (in period 2) over a set of panelists. For example:

$\begin{matrix}{s_{i,j}^{matched} = {\sum\limits_{k = 1}^{K}s_{i,j}^{k}}} & {{Equation}7}\end{matrix}$

v_(i,) ^(matched), v_(,j) ^(matched): total tuning minutes by matchedpanelists for program i in period 1 and for program j in period 2,respectively.

v_(i,) ^(matched), v_(,j) ^(matched): total tuning minutes by unmatchedpanelists for program i in period 1 and for program j in period 2,respectively.

In some examples, the unmatched panelist VoS estimator 135 determinesexample proportion-based VoS estimates for unmatched panelists, s_(i,j)^(prop), according to Equation 8:

$\begin{matrix}{s_{i,j}^{prop} = {s_{i,j}^{matched}*\sqrt{\frac{v_{,.}^{unmatched}}{v_{,.}^{matched}}*\frac{v_{.{,j}}^{unmatched}}{v_{.{,j}}^{matched}}}}} & {{Equation}8}\end{matrix}$

Thus, according to Equation 8, the unmatched panelist VoS estimator 135estimates a given proportion-based VoS value, s_(i,j) ^(prop) by (1)determining, based on the accessed panelist program viewing data 115, afirst matched tuning value (e.g., v_(i,) ^(matched)) representing anamount of tuning by the matched panelists to the first program in thefirst measurement period, (2) determining, based on the accessedpanelist program viewing data 115, a second matched tuning value (e.g.,v_(ij) ^(matched)) representing an amount of tuning by the matchedpanelists to the second program in the first measurement period, (3)determining, based on the accessed panelist program viewing data 115, afirst unmatched tuning value (e.g., v_(i,) ^(unmatched)) representing anamount of tuning by the unmatched panelists to the first program in thefirst measurement period, (4) determining, based on the accessedpanelist program viewing data 115, a second unmatched tuning value(e.g., v_(,j) ^(unmatched)) representing an amount of tuning by theunmatched panelists to the second program in the first measurementperiod, and (5) determining the second volume of switching value basedon a volume of switching value for matched panelists (e.g., s_(i,j)^(matched)), the first matched tuning value, the second matched tuningvalue, the first unmatched tuning value and the second unmatched tuningvalue. In the example of Equation 8, the unmatched panelist VoSestimator 135 determines the second volume of switching value based onthe first volume of switching value, the first matched tuning value, thesecond matched tuning value, the first unmatched tuning value and thesecond unmatched tuning value by (A) determining a scale factor (e.g.,corresponding to the term on the right side of the multiplication symbolin Equation 8) based on (i) a first ratio (e.g., v_(i,)^(unmatched)/v_(i,) ^(matched)) of the first unmatched tuning value tothe first ( matched tuning value and (ii) a second ratio (e.g., v_(,j)^(unmatched)/v_(,j) ^(matched)) of the second unmatched tuning value tothe second matched tuning value, and (B) multiplying the volume ofswitching value for matched panelists (e.g. s_(i,j) ^(matched)) by thescale factor to determine the volume of switching value for unmatchedpanelists (e.g., s_(i,j) ^(prop)). Furthermore, the unmatched panelistVoS estimator 135 determines the scale factor by determine a square rootof the first ratio multiplied by the second ratio.

The result of Equation 8 is a set of proportion-based VoS values,s_(i,j) ^(prop), representing a portion of a decreased amount of tuningby unmatched panelists to a first program, i, measured from a firstmeasurement period (e.g., period 1) to a second measurement period(e.g., period 2) to attribute to an increased amount of tuning by theunmatched panelists to a second television program, j, measured from thefirst measurement period (e.g., period 1) to the second measurementperiod (e.g., period 2). With this approach, the unmatched panelist VoSestimator 135 uses the volume of switching determined for matchedpanelists, but adjusted by the total viewing minutes of unmatchedpanelists in both measurement periods, to estimate the volume ofswitching for the unmatched panelists.

In some examples, the unmatched panelist VoS estimator 135 implements anexample balanced approach to estimate VoS values for unmatchedpanelists, s_(i,j) ^(balanced). With the proportion-based approach, therelative size of switching volumes from the matched panelists ismaintained, but rescaled to account for the total viewing minutes ofunmatched panelists. However, a potential issue with proportion-basedswitching volumes estimate is that they may not add up to the actualviewing minutes in the two periods. In other words, the followingproperties hold for matched panelists:

$\begin{matrix}{{\sum\limits_{j = 1}^{J}s_{i,j}} = v_{i,.}} & {{Equation}9}\end{matrix}$ $\begin{matrix}{{\sum\limits_{i = 1}^{I}s_{i,j}} = v_{.{,j}}} & {{Equation}10}\end{matrix}$

However, using the proportion-based approach, similar properties may nothold for the unmatched panelists. This may lead to possibleinconsistency in the ratings of individuals programs.

In some examples, the unmatched panelist VoS estimator 135 implementsthe balanced approach as given in Table 7:

TABLE 7 1. Apply proportion based method to estimate volume of switchingwithout forcing the total of the estimated program minutes to add up tothe known actual minutes. 2. Calculate the difference between true andestimated viewing minutes and assign the difference to the “Other TV andnon-TV” bucket (e.g., program 0) If the revised “Other TV and non-TV”bucket becomes negative, all other buckets for the programs in thatperiod are proportionally adjusted to add up to total actual viewingminutes The balanced VoS estimates for other buckets are the same asestimated values calculated by the proportion-based methodThe result is a set of balanced VoS values, s_(i,j) ^(balanced),representing a portion of a decreased amount of tuning by unmatchedpanelists to a first program, i, measured from a first measurementperiod (e.g., period 1) to a second measurement period (e.g., period 2)to attribute to an increased amount of tuning by the unmatched paneliststo a second television program, j, measured from the first measurementperiod (e.g., period 1) to the second measurement period (e.g., period2).

In some examples, the unmatched panelist VoS estimator 135 implements anexample non-linear optimization with constraint algorithm to estimateVoS values for unmatched panelists s_(i,j) ^(optimized). Thisoptimization method combines the benefits of both the proportion method(e.g., consistent pattern in switching volumes) and the balanced method(e.g., consistent total tuning/viewing minutes). To achieve these dualgoals, the optimization algorithm minimally adjusts s_(i,j) ^(prop) witha constraint that the new estimated VoS values add up to total tuningminutes at the program level in both periods for unmatched panelists.

To calculate the optimization-based switching minutes, s_(i,j)^(optimized) the unmatched panelist VoS estimator 135 of the illustratedexample uses the optimization function of Equation 11:

$\begin{matrix}{\min{\sum\limits_{i = 1}^{I}{\sum\limits_{j = 1}^{J}{❘{s_{i,j}^{optimized} - s_{i,j}^{prop}}❘}}}} & {{Equation}11}\end{matrix}$

with the constraints that, for each program in each period, the VoSshould add up to the total tuning/viewing minutes. Mathematically, theseconstraints are given by Equations 12 and 13:

$\begin{matrix}{{{{For}i} = {1{to}I}},{{\sum\limits_{j = 1}^{J}s_{i,j}^{optimized}} = v_{i,.}^{unmatched}}} & {{Equation}12}\end{matrix}$ $\begin{matrix}{{{{For}j} = {1{to}J}},{{\sum\limits_{i = 1}^{I}s_{i,j}^{optimized}} = v_{.{,j}}^{unmatched}}} & {{Equation}13}\end{matrix}$

Thus, according to Equations 11-13, the unmatched panelist VoS estimator135 estimates a given VoS value, s_(i,j) ^(optimized), based on (i)s_(i,j) ^(prop), which is the result of multiplying the volume ofswitching value for matched panelists by the scale factor according toEquation 8, (ii) a first constraint (e.g., from Equation 12) that afirst sum of volume of switching values (e.g., Σ_(j=1) ^(J)s_(i,j)^(optimized)) representing tuning by the unmatched panelists fromrespective ones of a first set of programs in the first measurementperiod to the second program in the second measurement period equals theunmatched tuning value v_(i,) ^(unmatched) and (iii) a second constraint(e.g., from Equation 13) that a second sum of volume of switching values(e.g., Σ_(i=1) ^(I)s_(i,j) ^(optimized)) representing tuning by theunmatched panelists from the first program in the first measurementperiod to respective ones of a second set of programs, including thesecond program, in the second measurement period equals the unmatchedtuning value v_(i,) ^(unmatched) The result is a set of optimized VoSvalues, s_(i,j) ^(optimized), representing a portion of a decreasedamount of tuning by unmatched panelists to a first program, i, measuredfrom a first measurement period (e.g., period 1) to a second measurementperiod (e.g., period 2) to attribute to an increased amount of tuning bythe unmatched panelists to a second television program, j, measured fromthe first measurement period (e.g., period 1) to the second measurementperiod (e.g., period 2).

In some examples, the unmatched panelist VoS estimator 135 implements anexample collapse algorithm to estimate VoS for unmatched panelists,s_(i,j) ^(collapse). In the example collapse algorithm, the unmatchedpanelist VoS estimator 135 treats all unmatched panelist viewing data asbeing associated with a virtual panelist, sums the viewing minutes forthis virtual panelist, and then applies the example algorithms describedabove for matched panelists to calculate the switching volumes, s_(i,j)^(collapse) for this virtual panelist. The result is a set of collapsedVoS values, s_(i,j) ^(collapse) representing a portion of a decreasedamount of tuning by unmatched panelists to a first program, i, measuredfrom a first measurement period (e.g., period 1) to a second measurementperiod (e.g., period 2) to attribute to an increased amount of tuning bythe unmatched panelists to a second television program, j, measured fromthe first measurement period (e.g., period 1) to the second measurementperiod (e.g., period 2).

In some examples, the unmatched panelist VoS estimator 135 implements anexample interaction algorithm to estimate VoS for unmatched panelists,s_(i,j) ^(interaction). In some such examples, the unmatched panelistVoS estimator 135 determines the VoS estimate for unmatched panelistss_(i,j) ^(interaction) according to Equations 14-17:

$\begin{matrix}{s_{i,j}^{interaction} = {s_{i,j}^{matched}*\frac{\frac{v_{i,.}^{unmatched}}{v_{i,.}^{matched}}*\frac{v_{.{,j}}^{unmatched}}{v_{.{,j}}^{matched}}}{\frac{v_{.{,{.{,.}}}}^{unmatched}}{v_{.{,{.{,.}}}}^{matched}}}}} & {{Equation}14}\end{matrix}$ $\begin{matrix}{{{{For}i} = {1{to}I}},{{\sum\limits_{j = 1}^{J}s_{i,j}} = v_{i,.}}} & {{Equation}15}\end{matrix}$ $\begin{matrix}{{{{For}j} = {1{to}J}},{{\sum\limits_{i = 1}^{I}s_{i,j}} = v_{.{,j}}}} & {{Equation}16}\end{matrix}$

For persons j=1 to J in period 1, i=1 to I in period 2 and programs k=1to K:

$\begin{matrix}{{{\sum\limits_{k = 1}^{K}{\sum\limits_{i = 1}^{I}s_{i,j,k}}} + {\sum\limits_{k = 1}^{K}{\sum\limits_{i = 1}^{I}s_{i,j,k}}}} = v_{.{,{.{,.}}}}} & {{Equation}17}\end{matrix}$

The result is a set of interaction VoS values, s_(i,j) ^(interaction)representing a portion of a decreased amount of tuning by unmatchedpanelists to a first program, i, measured from a first measurementperiod (e.g., period 1) to a second measurement period (e.g., period 2)to attribute to an increased amount of tuning by the unmatched paneliststo a second television program, j, measured from the first measurementperiod (e.g., period 1) to the second measurement period (e.g., period2).

In some examples, the unmatched panelist VoS estimator 135 implements anaverage of the VoS estimates determined for unmatched panelists usingthe example interaction algorithm and the example proportion-basedalgorithms disclosed above. For example, the unmatched panelist VoSestimator 135 can determine such a VoS estimate according to Equation18:

$\begin{matrix}{s_{i,j}^{{avg}_{i}{nterprop}} = \frac{s_{i,j}^{prop} + s_{i,j}^{interaction}}{2}} & {{Equation}18}\end{matrix}$

The result is a set of VoS values, s_(i,j) ^(avginterprop), representinga portion of a decreased amount of tuning by unmatched panelists to afirst program, i, measured from a first measurement period (e.g., period1) to a second measurement period (e.g., period 2) to attribute to anincreased amount of tuning by the unmatched panelists to a secondtelevision program, j, measured from the first measurement period (e.g.,period 1) to the second measurement period (e.g., period 2).

While an example manner of implementing the VoS estimator 100 isillustrated in FIG. 1 , one or more of the elements, processes and/ordevices illustrated in FIG. 1 may be combined, divided, re-arranged,omitted, eliminated and/or implemented in any other way. Further, theexample data retriever 105, the example panelist database 115, theexample panelist matcher 120, the example matched panelist biascorrector 125, the example matched panelist VoS calculator 130, theexample unmatched panelist VoS estimator 135, the example VoS outputgenerator 140, the example output device 150 and/or, more generally, theexample VoS estimator 100 of FIG. 1 may be implemented by hardware,software, firmware and/or any combination of hardware, software and/orfirmware. Thus, for example, any of the example data retriever 105, theexample panelist database 115, the example panelist matcher 120, theexample matched panelist bias corrector 125, the example matchedpanelist VoS calculator 130, the example unmatched panelist VoSestimator 135, the example VoS output generator 140, the example outputdevice 150 and/or, more generally, the example VoS estimator 100 couldbe implemented by one or more analog or digital circuit(s), logiccircuits, programmable processor(s), application specific integratedcircuit(s) (ASIC(s)), programmable logic device(s) (PLD(s)) and/or fieldprogrammable logic device(s) (FPLD(s)). When reading any of theapparatus or system claims of this patent to cover a purely softwareand/or firmware implementation, at least one of the example VoSestimator 100, the example data retriever 105, the example panelistdatabase 115, the example panelist matcher 120, the example matchedpanelist bias corrector 125, the example matched panelist VoS calculator130, the example unmatched panelist VoS estimator 135, the example VoSoutput generator 140 and/or the example output device 150 is/are herebyexpressly defined to include a non-transitory computer readable storagedevice or storage disk such as a memory, a digital versatile disk (DVD),a compact disk (CD), a Blu-ray disk, etc. including the software and/orfirmware. Further still, the example VoS estimator 100 may include oneor more elements, processes and/or devices in addition to, or insteadof, those illustrated in FIG. 1 , and/or may include more than one ofany or all of the illustrated elements, processes and devices.

Flowcharts representative of example machine readable instructions forimplementing the example VoS estimator 100, the example data retriever105, the example panelist database 115, the example panelist matcher120, the example matched panelist bias corrector 125, the examplematched panelist VoS calculator 130, the example unmatched panelist VoSestimator 135, the example VoS output generator 140 and/or the exampleoutput device 150 are shown in FIGS. 3-5 . In these examples, themachine readable instructions comprise one or more programs forexecution by a processor, such as the processor 612 shown in the exampleprocessor platform 600 discussed below in connection with FIG. 6 . Theone or more programs, or portion(s) thereof, may be embodied in softwarestored on a non-transitory computer readable storage medium such as aCD-ROM, a floppy disk, a hard drive, a digital versatile disk (DVD), aBlu-ray disk™, or a memory associated with the processor 612, but theentire program or programs and/or portions thereof could alternativelybe executed by a device other than the processor 612 and/or embodied infirmware or dedicated hardware (e.g., implemented by an ASIC, a PLD, anFPLD, discrete logic, etc.). Further, although the example program(s)is(are) described with reference to the flowcharts illustrated in FIGS.3-5 , many other methods of implementing the example VoS estimator 100,the example data retriever 105, the example panelist database 115, theexample panelist matcher 120, the example matched panelist biascorrector 125, the example matched panelist VoS calculator 130, theexample unmatched panelist VoS estimator 135, the example VoS outputgenerator 140 and/or the example output device 150 may alternatively beused. For example, with reference to the flowcharts illustrated in FIGS.3-5 , the order of execution of the blocks may be changed, and/or someof the blocks described may be changed, eliminated, combined and/orsubdivided into multiple blocks. Additionally or alternatively, any orall of the blocks may be implemented by one or more hardware circuits(e.g., discrete and/or integrated analog and/or digital circuitry, aField Programmable Gate Array (FPGA), an Application Specific Integratedcircuit (ASIC), a comparator, an operational-amplifier (op-amp), a logiccircuit, etc.) structured to perform the corresponding operation withoutexecuting software or firmware.

As mentioned above, the example processes of FIGS. 3-5 may beimplemented using coded instructions (e.g., computer and/or machinereadable instructions) stored on a non-transitory computer readablestorage medium such as a hard disk drive, a flash memory, a read-onlymemory (ROM), a compact disk (CD), a digital versatile disk (DVD), acache, a random-access memory (RAM) and/or any other storage device orstorage disk in which information is stored for any duration (e.g., forextended time periods, permanently, for brief instances, for temporarilybuffering, and/or for caching of the information). As used herein, theterm non-transitory computer readable storage medium is expresslydefined to include any type of computer readable storage device and/orstorage disk and to exclude propagating signals and to excludetransmission media. Including” and “comprising” (and all forms andtenses thereof) are used herein to be open ended terms. Thus, whenever aclaim lists anything following any form of “include” or “comprise”(e.g., comprises, includes, comprising, including, etc.), it is to beunderstood that additional elements, terms, etc. may be present withoutfalling outside the scope of the corresponding claim. As used herein,when the phrase “at least” is used as the transition term in a preambleof a claim, it is open-ended in the same manner as the terms“comprising” and “including” are open ended. Also, as used herein, theterms “computer readable” and “machine readable” are consideredequivalent unless indicated otherwise.

An example program 300 that may be executed to implement the example VoSestimator 100 of FIG. 1 is represented by the flowchart shown in FIG. 3. With reference to the preceding figures and associated writtendescriptions, the example program 300 of FIG. 3 begins execution atblocks 305 and 310. At block 305, the example data retriever 105accesses the example panelist database 115 based on input data 110specifying the first measurement period (P1) to aggregate tuning/viewingminutes for each panelist and for each program specified by the inputdata 110 to be the subject of the VoS analysis for the first measurementperiod. The resulting tuning/viewing minutes 315 for the firstmeasurement period are stored by the data retriever 105 in, for example,the panelist database 115. At block 310, the example data retriever 105accesses the example panelist database 115 based on input data 110specifying the second measurement period (P2) to aggregatetuning/viewing minutes for each panelist and for each program specifiedby the input data 110 to be the subject of the VoS analysis for thesecond measurement period. The resulting tuning/viewing minutes 320 forthe second measurement period are stored by the data retriever 105 in,for example, the panelist database 115.

At block 325, the example panelist matcher 120 determines, as describedabove, matched panelists represented in the both the tuning/viewingminutes 315 for the first measurement period and the tuning/viewingminutes 320 for the second measurement period. At block 330, the examplematched panelist bias corrector 125 removes matched panelists who do notmeet the unification threshold (e.g., 75%) in both measurement periods,as described above. At block 335, the matched panelist bias corrector125 performs bias correction, as described above. At block 340, the VoSestimator 100 determines whether the percentage of matching panelistssatisfies a first (e.g., lower) matching threshold (e.g., 20% or someother value). If the percentage of matching panelists fails to satisfythe first matching threshold (block 340), execution of the exampleprogram stops (block 345). However, if the percentage of matchingpanelists satisfies the first matching threshold (block 340), at block345, the VoS estimator 100 determines whether the percentage of matchingpanelists satisfies a second (e.g., upper) matching threshold (e.g., 90%or some other value). If the percentage of matching panelists satisfiesthe second matching threshold (block 350), at block 355, the VoSestimator 100 performs a VoS analysis based on just the tuning/viewingdata for the matching panelists. An example program that may be executedto perform the processing at block 355 is illustrated in FIG. 4 anddescribed in further detail below. However, if the percentage ofmatching panelists fails to satisfy the second matching threshold (block350), at block 360, the VoS estimator 100 performs a VoS analysis basedon the tuning/viewing data for the matching panelists and thetuning/viewing data for unmatched panelists. An example program that maybe executed to perform the processing at block 360 is illustrated inFIG. 5 and described in further detail below.

An example program 355P that may be executed to perform the processingat block 355 of FIG. 3 is represented by the flowchart shown in FIG. 4 .With reference to the preceding figures and associated writtendescriptions, the example program 355P of FIG. 4 begins execution atblock 405 at which the example matched panelist VoS calculator 130accesses tuning/viewing data for the matched panelists for the twomeasurement periods and the programs specified in the input data 420. Atblock 410, the matched panelist VoS calculator 130 calculates, asdescribed above, the VoS value s_(i,j) for the matched panelists forswitching between the different combinations (pairs) of programs i and jfrom the first measurement period to the second measurement period. Atblock 415, the matched panelist VoS calculator 130 tabulates theswitching matrices for the matched panelists, as described above. Atblock 420, the example VoS output generator 140 tabulates an aggregateswitching matrix including the aggregates matched panelist VoS values,s_(i,j) ^(matched) for the different combinations (pairs) of programs iand j from the first measurement period to the second measurementperiod. Execution of the example program 355P then ends. Additionally oralternatively, in some examples, at block 420, the VoS output generator140 outputs a Sankey diagram (e.g., corresponding to an output such asthe example VoS output 200 of FIG. 2 ) and/or other appropriategraphical output representing the aggregated matched panelist VoSvalues, s_(i,j) ^(matched) for the different combinations (pairs) ofprograms i and j from the first measurement period to the secondmeasurement period.

An example program 360P that may be executed to perform the processingat block 360 of FIG. 3 is represented by the flowchart shown in FIG. 5 .With reference to the preceding figures and associated writtendescriptions, the example program 360P of FIG. 4 begins by executingblocks 405, 410, 415 and 420 as described above with respect to FIG. 4 ,which results in the matched panelist VoS calculator 130 determining theswitching matrix for the matched panelists, which contain the aggregateVoS value s_(i,j) for the matched panelists for switching between thedifferent combinations (pairs) of programs i and j from the firstmeasurement period to the second measurement period. At blocks 505, 510and 515, the example unmatched panelist VoS estimator 135 accessestuning/viewing data for the unmatched panelists missing from one of thetwo measurement periods and for the programs specified in the input data420, aggregates the tuning/viewing data, and determines the values forv_(i,) ^(matched), v_(,j) ^(matched), which are the total tuning minutesby unmatched panelists for each program i in period 1 and for eachprogram j in period 2, respectively, as described above. At block 520,the unmatched panelist VoS estimator 135 determines the values forv_(i,) ^(matched), v_(,j) ^(matched), which are the total tuning minutesby matched panelists for each program i in period 1 and for each programj in period 2, respectively.

At block 525, the unmatched panelist VoS estimator 135 determines theexample proportion-based VoS estimate for unmatched panelists, s_(i,j)^(prop), as described above. At blocks 530 and 535, the unmatchedpanelist VoS estimator 135 performs the non-linear optimization withconstraint algorithm to estimate VoS values for unmatched panelists,s_(i,j) ^(optimized), as described above. In some examples, if thenon-linear optimization with constraint algorithm fails to converge(block 540), execution of the example program 360P stops (block 545). Insome examples, further iterations of blocks 530 and 535 may be performedwith relaxed constraints to provide more opportunities for thenon-linear optimization with constraint algorithm to converge. In somesuch examples, if the non-linear optimization with constraint algorithmfails to converge after these further iterations (block 540), executionof the example program 360P then stops (block 545).

However, if the non-linear optimization with constraint algorithmconverges (block 540), then at block 550, the unmatched panelist VoSestimator 135 tabulates an estimated switching matrix for the unmatchedpanelists, which contains the estimated VoS values for unmatchedpanelists, s_(i,j) ^(optimized,) for the different combinations (pairs)of programs i and j from the first measurement period to the secondmeasurement period. At block 560, the VoS output generator 140 combines(e.g., adds) the switching matrix determined at blocks 415 and 420 forthe matched panelists and the estimated switching matrix determined atblock 550 for the unmatched panelists. At block 565, the VoS outputgenerator 140 outputs the resulting total switching matrix (e.g., in theform of a Sankey diagram, as described above). In some examples, theprocessing associated with blocks 530-545 is omitted and controlproceeds from block 525 to block 550. In some examples, the processingassociated with blocks 530-545 is modified to implement one or more ofthe other example techniques described above for estimating VoS forunmatched panelists.

FIG. 6 is a block diagram of an example processor platform 600 capableof executing the instructions of FIGS. 3, 4 and/or 5 to implement theexample VoS estimator 100 of FIG. 1 . The processor platform 600 can be,for example, a server, a personal computer, a mobile device (e.g., acell phone, a smart phone, a tablet such as an iPad™), a personaldigital assistant (PDA), an Internet appliance, a DVD player, a CDplayer, a digital video recorder, a Blu-ray player, a gaming console, apersonal video recorder, a set top box a digital camera, or any othertype of computing device.

The processor platform 600 of the illustrated example includes aprocessor 612. The processor 612 of the illustrated example is hardware.For example, the processor 612 can be implemented by one or moreintegrated circuits, logic circuits, microprocessors or controllers fromany desired family or manufacturer. In the illustrated example of FIG. 6, the processor 612 is configured via example instructions 632, whichinclude the example instructions of FIGS. 3, 4 and/or 5 , to implementthe example data retriever 105, the example panelist matcher 120, theexample matched panelist bias corrector 125, the example matchedpanelist VoS calculator 130, the example unmatched panelist VoSestimator 135 and/or the example VoS output generator 140 of FIG. 1 .

The processor 612 of the illustrated example includes a local memory 613(e.g., a cache). The processor 612 of the illustrated example is incommunication with a main memory including a volatile memory 614 and anon-volatile memory 616 via a link 618. The link 618 may be implementedby a bus, one or more point-to-point connections, etc., or a combinationthereof. The volatile memory 614 may be implemented by SynchronousDynamic Random Access Memory (SDRAM), Dynamic Random Access Memory(DRAM), RAMBUS Dynamic Random Access Memory (RDRAM) and/or any othertype of random access memory device. The non-volatile memory 616 may beimplemented by flash memory and/or any other desired type of memorydevice. Access to the main memory 614, 616 is controlled by a memorycontroller.

The processor platform 600 of the illustrated example also includes aninterface circuit 620. The interface circuit 620 may be implemented byany type of interface standard, such as an Ethernet interface, auniversal serial bus (USB), and/or a PCI express interface.

In the illustrated example, one or more input devices 622 are connectedto the interface circuit 620. The input device(s) 622 permit(s) a userto enter data and commands into the processor 612. The input device(s)can be implemented by, for example, an audio sensor, a microphone, acamera (still or video), a keyboard, a button, a mouse, a touchscreen, atrack-pad, a trackball, a trackbar (such as an isopoint), a voicerecognition system and/or any other human-machine interface. Also, manysystems, such as the processor platform 600, can allow the user tocontrol the computer system and provide data to the computer usingphysical gestures, such as, but not limited to, hand or body movements,facial expressions, and face recognition.

One or more output devices 624 are also connected to the interfacecircuit 620 of the illustrated example. The output devices 624 can beimplemented, for example, by display devices (e.g., a light emittingdiode (LED), an organic light emitting diode (OLED), a liquid crystaldisplay, a cathode ray tube display (CRT), a touchscreen, a tactileoutput device, a printer and/or speakers). The interface circuit 620 ofthe illustrated example, thus, typically includes a graphics drivercard, a graphics driver chip or a graphics driver processor. In theillustrated example of FIG. 6 , the output device(s) 624 implement theexample output device 150 of FIG. 1 .

The interface circuit 620 of the illustrated example also includes acommunication device such as a transmitter, a receiver, a transceiver, amodem and/or network interface card to facilitate exchange of data withexternal machines (e.g., computing devices of any kind) via a network626 (e.g., an Ethernet connection, a digital subscriber line (DSL), atelephone line, coaxial cable, a cellular telephone system, etc.).

The processor platform 600 of the illustrated example also includes oneor more mass storage devices 628 for storing software and/or data.Examples of such mass storage devices 628 include floppy disk drives,hard drive disks, compact disk drives, Blu-ray disk drives, RAID(redundant array of independent disks) systems, and digital versatiledisk (DVD) drives. In some examples, the mass storage device 628 mayimplement the example panelist database 115 of FIG. 1 . Additionally oralternatively, in some examples, the volatile memory 614 may implementthe example panelist database 115 of FIG. 1

Coded instructions 632 corresponding to the instructions of FIGS. 3, 4and/or 5 may be stored in the mass storage device 628, in the volatilememory 614, in the non-volatile memory 616, in the local memory 613and/or on a removable tangible computer readable storage medium, such asa CD or DVD 636.

From the foregoing, it will be appreciated that example methods,apparatus and articles of manufacture have been disclosed that estimatevolume of switching among television programs over two measurementperiods of interest for an audience measurement panel. Unlike prior VoSanalysis techniques, example VoS analysis techniques disclosed hereinare able to utilize incomplete panelist viewing data in the VoSanalysis. As such, example VoS analysis techniques disclosed hereinimprove VoS estimates by including panelists who are in the audiencemeasurement panel for just a portion of the two measurement periods ofinterest.

Although certain example methods, apparatus and articles of manufacturehave been disclosed herein, the scope of coverage of this patent is notlimited thereto. On the contrary, this patent covers all methods,apparatus and articles of manufacture fairly falling within the scope ofthe claims of this patent.

What is claimed is:
 1. An apparatus to determine volume of switchingamong television programs, the apparatus comprising: at least onememory; computer readable instructions; and processor circuitry toexecute the instructions to at least: process first viewing dataassociated with a first measurement time period and second viewing dataassociated with a second measurement time period to identify a first setof panelists represented in both the first viewing data and the secondviewing data; in response to a size of the first set of panelistssatisfying both a first threshold and a second threshold, estimate thevolume of switching among the television programs from the firstmeasurement time period to the second measurement time period based on afirst subset of the first viewing data associated with the first set ofpanelists and a second subset of the second viewing data associated withthe first set of panelists; and in response to the size of the first setof panelists satisfying the first threshold but not satisfying thesecond threshold, estimate the volume of switching among the televisionprograms from the first measurement time period to the secondmeasurement time period based on the first subset of the first viewingdata, the second subset of the second viewing data, a third subset ofthe first viewing data associated with a second set of panelistsdifferent from the first set of panelists, and a fourth subset of thesecond viewing data associated with the second set of panelists.
 2. Theapparatus of claim 1, wherein the first set of panelists includes afirst panelist, and the processor circuitry is to include the firstpanelist in the first set of panelists when (i) a respective portion ofthe first viewing data associated with the first panelist is valid forat least a threshold percentage of the first measurement time period,and (ii) a respective portion of the second viewing data associated withthe first panelist is valid for at least the threshold percentage of thesecond measurement time period.
 3. The apparatus of claim 2, wherein thesecond set of panelists includes a second panelist, and the processorcircuitry is to include the second panelist in the second set ofpanelists when one but not both of (i) a respective portion of the firstviewing data associated with the second panelist is valid for at leastthe threshold percentage of the first measurement time period, or (ii) arespective portion of the second viewing data associated with the firstpanelist is valid for at least the threshold percentage of the secondmeasurement time period.
 4. The apparatus of claim 1, wherein the secondthreshold is larger than the first threshold.
 5. The apparatus of claim1, wherein the processor circuitry is not to estimate the volume ofswitching among the television programs from the first measurement timeperiod to the second measurement time period in response to adetermination that the size of the first set of panelists does notsatisfy the first threshold.
 6. The apparatus of claim 1, wherein thefirst set of panelists includes a first panelist, and the processorcircuitry is to determine a first volume of switching value associatedwith the first panelist, the first volume of switching value torepresent a portion of a decrease in viewing of a first televisionprogram to attribute to an increase in viewing of a second televisionprogram, the decrease in viewing of the first television programmeasured from the first measurement time period to the secondmeasurement time period, the increase in viewing of the secondtelevision program measured from the first measurement time period tothe second measurement time period.
 7. The apparatus of claim 6, whereinto determine the first volume of switching value, the processorcircuitry is to: determine a ratio of (i) the increase in viewing of thesecond television program to (ii) a total increase in viewing of ones ofthe television programs having increased viewing from the firstmeasurement time period to the second measurement time period; and scalethe decrease in viewing of the first television program by the ratio. 8.At least one non-transitory computer readable medium comprising computerreadable instructions that, when executed, cause at least one processorto at least: process first viewing data associated with a firstmeasurement time period and second viewing data associated with a secondmeasurement time period to identify a first set of panelists representedin both the first viewing data and the second viewing data; in responseto a size of the first set of panelists satisfying both a firstthreshold and a second threshold, estimate volume of switching amongtelevision programs from the first measurement time period to the secondmeasurement time period based on a first subset of the first viewingdata associated with the first set of panelists and a second subset ofthe second viewing data associated with the first set of panelists; andin response to the size of the first set of panelists satisfying thefirst threshold but not satisfying the second threshold, estimate thevolume of switching among the television programs from the firstmeasurement time period to the second measurement time period based onthe first subset of the first viewing data, the second subset of thesecond viewing data, a third subset of the first viewing data associatedwith a second set of panelists different from the first set ofpanelists, and a fourth subset of the second viewing data associatedwith the second set of panelists.
 9. The at least one non-transitorycomputer readable medium of claim 8, wherein the first set of panelistsincludes a first panelist, and the instructions are to cause the atleast one processor to include the first panelist in the first set ofpanelists when (i) a respective portion of the first viewing dataassociated with the first panelist is valid for at least a thresholdpercentage of the first measurement time period, and (ii) a respectiveportion of the second viewing data associated with the first panelist isvalid for at least the threshold percentage of the second measurementtime period.
 10. The at least one non-transitory computer readablemedium of claim 9, wherein the second set of panelists includes a secondpanelist, and the instructions are to cause the at least one processorto include the second panelist in the second set of panelists when onebut not both of (i) a respective portion of the first viewing dataassociated with the second panelist is valid for at least the thresholdpercentage of the first measurement time period, or (ii) a respectiveportion of the second viewing data associated with the first panelist isvalid for at least the threshold percentage of the second measurementtime period.
 11. The at least one non-transitory computer readablemedium of claim 8, wherein the second threshold is larger than the firstthreshold.
 12. The at least one non-transitory computer readable mediumof claim 8, wherein the instructions are to cause the at least oneprocessor not to estimate the volume of switching among the televisionprograms from the first measurement time period to the secondmeasurement time period in response to a determination that the size ofthe first set of panelists does not satisfy the first threshold.
 13. Theat least one non-transitory computer readable medium of claim 8, whereinthe first set of panelists includes a first panelist, and theinstructions are to cause the at least one processor to determine afirst volume of switching value associated with the first panelist, thefirst volume of switching value to represent a portion of a decrease inviewing of a first television program to attribute to an increase inviewing of a second television program, the decrease in viewing of thefirst television program measured from the first measurement time periodto the second measurement time period, the increase in viewing of thesecond television program measured from the first measurement timeperiod to the second measurement time period.
 14. The at least onenon-transitory computer readable medium of claim 13, wherein todetermine the first volume of switching value, the instructions are tocause the at least one processor to: determine a ratio of (i) theincrease in viewing of the second television program to (ii) a totalincrease in viewing of ones of the television programs having increasedviewing from the first measurement time period to the second measurementtime period; and scale the decrease in viewing of the first televisionprogram by the ratio.
 15. A method comprising: processing first viewingdata associated with a first measurement time period and second viewingdata associated with a second measurement time period to identify afirst set of panelists represented in both the first viewing data andthe second viewing data; in response to a size of the first set ofpanelists satisfying both a first threshold and a second threshold,estimating, by executing an instruction with at least one processor,volume of switching among television programs from the first measurementtime period to the second measurement time period based on a firstsubset of the first viewing data associated with the first set ofpanelists and a second subset of the second viewing data associated withthe first set of panelists; and in response to the size of the first setof panelists satisfying the first threshold but not satisfying thesecond threshold, estimating, by executing an instruction with the atleast one processor, the volume of switching among the televisionprograms from the first measurement time period to the secondmeasurement time period based on the first subset of the first viewingdata, the second subset of the second viewing data, a third subset ofthe first viewing data associated with a second set of panelistsdifferent from the first set of panelists, and a fourth subset of thesecond viewing data associated with the second set of panelists.
 16. Themethod of claim 15, wherein the first set of panelists includes a firstpanelist, and further including associating the first panelist with thefirst set of panelists when (i) a respective portion of the firstviewing data associated with the first panelist is valid for at least athreshold percentage of the first measurement time period, and (ii) arespective portion of the second viewing data associated with the firstpanelist is valid for at least the threshold percentage of the secondmeasurement time period.
 17. The method of claim 16, wherein the secondset of panelists includes a second panelist, and further includingassociating the second panelist with the second set of panelists whenone but not both of (i) a respective portion of the first viewing dataassociated with the second panelist is valid for at least the thresholdpercentage of the first measurement time period, or (ii) a respectiveportion of the second viewing data associated with the first panelist isvalid for at least the threshold percentage of the second measurementtime period.
 18. The method of claim 15, wherein the second threshold islarger than the first threshold.
 19. The method of claim 15, furtherincluding not estimating the volume of switching among the televisionprograms from the first measurement time period to the secondmeasurement time period in response to a determination that the size ofthe first set of panelists does not satisfy the first threshold.
 20. Themethod of claim 15, wherein the first set of panelists includes a firstpanelist, and further including determining a first volume of switchingvalue associated with the first panelist, the first volume of switchingvalue to represent a portion of a decrease in viewing of a firsttelevision program to attribute to an increase in viewing of a secondtelevision program, the decrease in viewing of the first televisionprogram measured from the first measurement time period to the secondmeasurement time period, the increase in viewing of the secondtelevision program measured from the first measurement time period tothe second measurement time period.